Lesson: GMAT Counting Strategies - Part I

Comment on GMAT Counting Strategies - Part I

Hi Brent,

For this question - https://gmatclub.com/forum/four-women-and-three-men-must-be-seated-in-a-row-for-a-group-photo-238447.html

I am not able to understand the solution despite reading all of them especially the part "For each arrangement of 4 women, there are 5 spaces where the 3 men can be placed."

If possible, please further detail out the solution. Also, is it possible to solve using the compliment method?

Warm Regards,
Pritish
gmat-admin's picture

Question link: https://gmatclub.com/forum/four-women-and-three-men-must-be-seated-in-a-...

This is a super hard question. In fact, I'd say it has a 750+ level of difficulty.

Once we've arranged the 4 women (in 4! ways) we can ensure that the men are separated my only allowing each man to be seated BETWEEN two women, or on the far-left or far-right seats.

So, in the diagram _ W _ W _ W _ W _, the blanks represent the only allowable places to seat each man.
There are 5 allowable spaces where each man can be seated.

So, there are 5 allowable places to seat the first man
There are 4 allowable places to seat the second man
And there are 3 allowable places to seat the second man.

At this point, we have 2 remaining locations (aka chairs) that are unfilled.
For example, we may have: MWMW_WMW_
So, we just throw those unfilled chairs away to get: MWMWWMW

ASIDE: Solving this question via the compliment would be a nightmare since there are many different ways to break the rule about 2 men not sitting together.

Cheers,
Brent

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